The President of the United States of America has the power of the veto, which means he can stop legislation from becoming law. The president's veto power is just one of the many separations of power, or "checks and balances" of the United States government. The legislative, judicial, and executive branches make up our government's separation of power.
Both the House of Representatives and Senate (collectively known as Congress) vote on bills to become law. When the House of Representatives proposes and then passes a bill, it continues on to the Senate. If the Senate also passes the bill, then the bill continues on to the president, who either signs it into law, or does not sign and vetoes the bill.
Think of it in another way: Let's say your brother is the House of Representatives, you are the Senate and your parents are the president (of your family, anyhow). Your brother proposes and passes a bill stating that you and your brother should be given $20 in allowance from your parents on weekly basis. The bill is sent along for your vote, and of course you also pass it. In order for this family bill to become "law," your parents (the president) must pass it. However, they both felt it was too large of an allowance, so they veto the bill. Your brother then revises the bill, for $10 a week in allowance, and you both pass the bill. Your parents feel that this is more acceptable, and sign the bill, making it a "law."
Your parents "veto" power in this example is essentially the same power the president has over Congress.
You can find out more about how a bill becomes law and the president's veto power at the following links: